Malament–Hogarth Machines and Tait’s Axiomatic Conception of Mathematics
In this paper I will argue that Tait’s axiomatic conception of mathematics implies that it is in principle impossible to be justified in believing a mathematical statement without being justified in believing that statement to be provable. I will then show that there are possible courses of experience which would justify acceptance of a mathematical statement without justifying belief that this statement is provable.
KeywordsMathematical Knowledge Mathematical Practice Epistemic Justification Mathematical Truth Peano Arithmetic
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